Integrable sub-Riemannian geodesic flows on the special orthogonal group
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908492408815616 |
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| author | Bravo-Doddoli, Alejandro Arathoon, Philip Bloch, Anthony M. |
| author_facet | Bravo-Doddoli, Alejandro Arathoon, Philip Bloch, Anthony M. |
| contents | We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metric defined on this distribution are completely integrable. Our argument is an adaptation of the method used to establish integrability of the Riemannian metric arising from the $n$-dimensional rigid body: namely, by exhibiting a Lax pair and bi-Hamiltonian structure for the reduced equations of motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable sub-Riemannian geodesic flows on the special orthogonal group Bravo-Doddoli, Alejandro Arathoon, Philip Bloch, Anthony M. Differential Geometry Dynamical Systems 37J35, 17B80, 53C17, 70G65 We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metric defined on this distribution are completely integrable. Our argument is an adaptation of the method used to establish integrability of the Riemannian metric arising from the $n$-dimensional rigid body: namely, by exhibiting a Lax pair and bi-Hamiltonian structure for the reduced equations of motion. |
| title | Integrable sub-Riemannian geodesic flows on the special orthogonal group |
| topic | Differential Geometry Dynamical Systems 37J35, 17B80, 53C17, 70G65 |
| url | https://arxiv.org/abs/2411.09008 |